In this paper, different aspects of lossy soils including ionization, and dispersion on the Grounding Potential Rise (GPR) of multiple vertical rods under lightning return strokes are simultaneously investigated. In all analyses, an efficient modeling approach called Improved Multiconductor Transmission Line (IMTL) is adopted. In the case of single rod, numerical analyses show that when there are the two mentioned aspects, GPR is decreased further with respect to situations where only one aspect is considered. This reduction is considered more for highly resistive soils, and fast-fronted lightning currents. In the case of multiple rods, however, it is placed between the GPRs of only-ionized and only-dispersive soils. Moreover, sensitivity analysis on the non-homogeneity effect in ionized and dispersive soils is carried out. Finally, comprehensively predicting formulae for GPR of multiple rods versus parameters of lightning current, lossy soil and rod are extracted.